Optical Tip Clearance Measurements as a Tool for Rotating Disk Characterization

An experimental investigation on the vibrational behavior of a rotating disk by means of three optical fiber sensors is presented. The disk, which is a scale model of the real disk of an aircraft engine, was assembled in a wind tunnel in order to simulate real operation conditions. The pressure difference between the upstream and downstream sides of the disk causes an airflow that might force the disk to vibrate. To characterize this vibration, a set of parameters was determined by measuring the tip clearance of the disk: the amplitude, the frequency and the number of nodal diameters in the disk. All this information allowed the design of an upgraded prototype of the disk, whose performance was also characterized by the same method. An optical system was employed for the measurements, in combination with a strain gauge mounted on the disk surface, which served to confirm the results obtained. The data of the strain gauge coincided closely with those provided by the optical fiber sensors, thus demonstrating the suitability of this innovative technique to evaluate the vibrational behavior of rotating disks.


Introduction
The operation of multiple devices, such as computer hard disks or circular saws, is based on rotating disks [1]. During operation, these rotating disks may experience vibrations that reduce their performance and service lives. Such vibrations could be due to several reasons, e.g., tolerances in the manufacturing process, aging, or some asymmetry in the disk. Vibrations of critical amplitudes cause a reduction in the reliability of the devices, which may undergo failures due to fatigue [2]. Therefore, there is a great interest in exploring techniques that allow the monitorization and characterization of the vibrational behavior of rotating disks [3][4][5].
In this paper, we report on our evaluation works related to the vibrational behavior of a rotating disk that is a scale model of a real disk of an aircraft engine. Such evaluation was carried out by means of a non-contact method employing three optical fiber sensors (OFSs) [6,7]. Its interest lies in the fact that reliability of aircraft components is of capital importance, since a failure in one of them could lead to a catastrophic situation. Although it is completely unfeasible to totally avoid the chance of disk failures, nowadays the number of disk flaws has been considerably reduced by means of melting-process controls and non-destructive-inspection techniques [8]. Up to now, these have

Experimental Set-Up
The experiments were carried out in the transonic wind tunnel at Aeronautical Technologies Center (CTA). The CTA's rotating-turbine-test facility is a continuous transonic-flow-test bed with an atmospheric inlet/outlet. The level of pressure/vacuum, the temperature and the mass flow are individually regulated, so that Mach and Reynolds numbers can be independently modified.
The supply and exit air conditions in the test section are achieved by employing two centrifugal compressor and vacuum groups, which are run, respectively, by electrical motors of 3.7 MW and 5 MW. The compressors are able to supply a maximum mass flow of 18 kg/s, with a maximum supply pressure up to 4.5 bar, a minimum exit pressure of 0.3 bar, and a temperature regulation from atmospheric temperature up to 160 • C. The turbine power is transmitted by a single shaft (up to 7800 rpm) to a dynamometer (up to 11,000 rpm 3.3 MW). The test section has a diameter of 1 m. A schematic of the facility is included in Figure 1. The data acquisition system is able to acquire up to 800 pressure channels, 200 temperature channels and 28 vibration signals. It can also acquire 20 rotating signals and it incorporates high accuracy torque machines and duplicated rpm and mass flow measurements. More information regarding the tunnel can be found in [18].
As mentioned before, the main objective of the tests was to characterize the vibrational behavior of the rotating disk under test. Specifically, we needed to know the vibration frequencies and the number of nodal diameters (NDs) of the disk at those frequencies. A nodal diameter can be defined as the line of stationary points that separates parts of the disk vibrating out of phase with respect to each other. The concept of nodal diameter is represented in Figure 2, where we can see a disk vibrating with one, two and three nodal diameters.  This information enabled the design of an improved second prototype with damped vibrations. In order to obtain results from the disk that correspond to real working conditions, this was assembled in a wind tunnel where a pressure difference was established between both sides of the disk, ranging from 2 to 3 bar. As well as evaluating the case when the disk is not rotating, the disk's performance was analyzed at its nominal rotating speed (RPMnominal), and at 1.5 and 2 times RPMnominal. In order to get these rotating speeds, the shaft was driven by a 100 kW electric motor and it was controlled by means of a hydraulic brake.
Three OFSs were installed in the wind tunnel to carry out TC measurements. They were arranged at an angle of 120° between them and separated by 4.75 mm from the disk edge (see Figure 3). These reflective intensity-modulated OFSs were originally developed to perform TC measurements in turbines [19]. Their main component is a trifurcated bundle of optical fibers whose particular design allows us to transmit the light from a laser to the target, and to collect the reflected light which is employed to calculate the distance from the bundle tip to the target. All the components and the performance characteristics of the sensors have been described in [20]. Each of the three sensors provides two output signals, whose quotient serves us to obtain the distance to the target according to a calibration curve. This method provides immunity to the fluctuations of the light source, to changes in the reflectivity of the target surface, and to losses or misalignments between the sensor probe and the target [21]. Due to the high number of sensors and transducers needed to measure the temperature and pressure in multiple points of the wind tunnel, only three inputs of the acquisition system were available. In this situation, we have two options: (a) one sensor with two output signals; or (b) three sensors, each one with a single output, (see Figure 3). We chose the latter option because it implied a loss of accuracy of only about ±8% in the measured amplitude with respect to the first option. This loss of accuracy does not affect the detection of the vibration frequency, which was the   This information enabled the design of an improved second prototype with damped vibrations. In order to obtain results from the disk that correspond to real working conditions, this was assembled in a wind tunnel where a pressure difference was established between both sides of the disk, ranging from 2 to 3 bar. As well as evaluating the case when the disk is not rotating, the disk's performance was analyzed at its nominal rotating speed (RPMnominal), and at 1.5 and 2 times RPMnominal. In order to get these rotating speeds, the shaft was driven by a 100 kW electric motor and it was controlled by means of a hydraulic brake.
Three OFSs were installed in the wind tunnel to carry out TC measurements. They were arranged at an angle of 120° between them and separated by 4.75 mm from the disk edge (see Figure 3). These reflective intensity-modulated OFSs were originally developed to perform TC measurements in turbines [19]. Their main component is a trifurcated bundle of optical fibers whose particular design allows us to transmit the light from a laser to the target, and to collect the reflected light which is employed to calculate the distance from the bundle tip to the target. All the components and the performance characteristics of the sensors have been described in [20]. Each of the three sensors provides two output signals, whose quotient serves us to obtain the distance to the target according to a calibration curve. This method provides immunity to the fluctuations of the light source, to changes in the reflectivity of the target surface, and to losses or misalignments between the sensor probe and the target [21]. Due to the high number of sensors and transducers needed to measure the temperature and pressure in multiple points of the wind tunnel, only three inputs of the acquisition system were available. In this situation, we have two options: (a) one sensor with two output signals; or (b) three sensors, each one with a single output, (see Figure 3). We chose the latter option because it implied a loss of accuracy of only about ±8% in the measured amplitude with respect to the first option. This loss of accuracy does not affect the detection of the vibration frequency, which was the This information enabled the design of an improved second prototype with damped vibrations. In order to obtain results from the disk that correspond to real working conditions, this was assembled in a wind tunnel where a pressure difference was established between both sides of the disk, ranging from 2 to 3 bar. As well as evaluating the case when the disk is not rotating, the disk's performance was analyzed at its nominal rotating speed (RPM nominal ), and at 1.5 and 2 times RPM nominal . In order to get these rotating speeds, the shaft was driven by a 100 kW electric motor and it was controlled by means of a hydraulic brake.
Three OFSs were installed in the wind tunnel to carry out TC measurements. They were arranged at an angle of 120 • between them and separated by 4.75 mm from the disk edge (see Figure 3). These reflective intensity-modulated OFSs were originally developed to perform TC measurements in turbines [19]. Their main component is a trifurcated bundle of optical fibers whose particular design allows us to transmit the light from a laser to the target, and to collect the reflected light which is employed to calculate the distance from the bundle tip to the target. All the components and the performance characteristics of the sensors have been described in [20]. Each of the three sensors provides two output signals, whose quotient serves us to obtain the distance to the target according to a calibration curve. This method provides immunity to the fluctuations of the light source, to changes in the reflectivity of the target surface, and to losses or misalignments between the sensor probe and the target [21]. Due to the high number of sensors and transducers needed to measure the temperature and pressure in multiple points of the wind tunnel, only three inputs of the acquisition system were available. In this situation, we have two options: (a) one sensor with two output signals; or (b) three sensors, each one with a single output, (see Figure 3). We chose the latter option because it implied a loss of accuracy of only about ±8% in the measured amplitude with respect to the first option. This loss of accuracy does not affect the detection of the vibration frequency, which was the main goal of the tests, since both options would yield the same frequency, although with different amplitudes. Besides, the use of three sensors allows us to calculate the eccentricity of the disk.
The probe fixed to the casing ( Figure 3) does not detect the real vibration frequency of the disk when it is rotating, but a modulated frequency instead. The reason is that the measured frequency is modulated by the rotational speed and by the set of NDs excited in the disk, according to the following equation [22]: where f os is the frequency detected by the OFS, f disk is the vibration frequency of the disk, f r is the rotational frequency, and ND is the number of nodal diameters. In order to check the ability of the sensors to detect the vibration frequency and to obtain the NDs of the disk, a strain gauge was instrumented on the disk surface.
Sensors 2017, 17, 165 4 of 12 main goal of the tests, since both options would yield the same frequency, although with different amplitudes. Besides, the use of three sensors allows us to calculate the eccentricity of the disk. The probe fixed to the casing ( Figure 3) does not detect the real vibration frequency of the disk when it is rotating, but a modulated frequency instead. The reason is that the measured frequency is modulated by the rotational speed and by the set of NDs excited in the disk, according to the following equation [22]: where fos is the frequency detected by the OFS, fdisk is the vibration frequency of the disk, fr is the rotational frequency, and ND is the number of nodal diameters. In order to check the ability of the sensors to detect the vibration frequency and to obtain the NDs of the disk, a strain gauge was instrumented on the disk surface. The calibration process of the OFSs is illustrated in Figure 4. It is the flattest part of the disk that is illuminated, so as to get the most stable signal, taking into account that the disk will flutter. To obtain the calibration curve of each sensor, the values of the voltage of the photodetector were successively stored as the tip of the probe was separated from the disk surface in steps of 10 µ m. This procedure was repeated three times to obtain a calibration curve in a range of distances up to 10 mm, and the results were averaged to obtain a more accurate calibration. Since the expected amplitude of the vibration was 0.25 mm, the resulting curve was linearized in the interval 4.5-5 mm to obtain the following calibration curves (represented in Figure 5): where d is the distance to the disk (in mm) and V is the voltage of the photodetector (in V).
As can be seen in Figure 4b, the disk incorporates a flange whose depth is 4.57 mm. Therefore, to obtain the real TC of the disk, this distance must be subtracted from the value provided by Equations (2)-(4). The calibration process of the OFSs is illustrated in Figure 4. It is the flattest part of the disk that is illuminated, so as to get the most stable signal, taking into account that the disk will flutter. To obtain the calibration curve of each sensor, the values of the voltage of the photodetector were successively stored as the tip of the probe was separated from the disk surface in steps of 10 µm. This procedure was repeated three times to obtain a calibration curve in a range of distances up to 10 mm, and the results were averaged to obtain a more accurate calibration. Since the expected amplitude of the vibration was 0.25 mm, the resulting curve was linearized in the interval 4.5-5 mm to obtain the following calibration curves (represented in Figure 5): where d is the distance to the disk (in mm) and V is the voltage of the photodetector (in V). As can be seen in Figure 4b, the disk incorporates a flange whose depth is 4.57 mm. Therefore, to obtain the real TC of the disk, this distance must be subtracted from the value provided by Equations (2)-(4).  The signals of all the sensors involved in the tests were acquired using the dynamic-signal-acquisition module PXI-4472 from National Instruments. They were sampled at 25 k samples/s and the complete signal-acquisition process for each signal lasted for 5 s (125,000 samples). For the OFS, Matlab was used to obtain the Fast Fourier Transform (FFT) of each signal with a frequency resolution of 0.2 Hz. However, the FFT of the signal from the strain gauge was provided by the acquisition program employed in CTA with a frequency resolution of 2 Hz.
To determine the uncertainty of the measurements of the three OFSs, some tests were carried out in our laboratory. The tip of the probe was placed 4.5 mm away from the disk edge and it was moved outwards along 1 mm in 25-µm steps using a linear stage. In each step, the voltage of the photodetector was recorded. This procedure was repeated three times for each distance, and the  The signals of all the sensors involved in the tests were acquired using the dynamic-signal-acquisition module PXI-4472 from National Instruments. They were sampled at 25 k samples/s and the complete signal-acquisition process for each signal lasted for 5 s (125,000 samples). For the OFS, Matlab was used to obtain the Fast Fourier Transform (FFT) of each signal with a frequency resolution of 0.2 Hz. However, the FFT of the signal from the strain gauge was provided by the acquisition program employed in CTA with a frequency resolution of 2 Hz.
To determine the uncertainty of the measurements of the three OFSs, some tests were carried out in our laboratory. The tip of the probe was placed 4.5 mm away from the disk edge and it was moved outwards along 1 mm in 25-µm steps using a linear stage. In each step, the voltage of the photodetector was recorded. This procedure was repeated three times for each distance, and the The signals of all the sensors involved in the tests were acquired using the dynamic-signal-acquisition module PXI-4472 from National Instruments. They were sampled at 25 k samples/s and the complete signal-acquisition process for each signal lasted for 5 s (125,000 samples). For the OFS, Matlab was used to obtain the Fast Fourier Transform (FFT) of each signal with a frequency resolution of 0.2 Hz. However, the FFT of the signal from the strain gauge was provided by the acquisition program employed in CTA with a frequency resolution of 2 Hz.
To determine the uncertainty of the measurements of the three OFSs, some tests were carried out in our laboratory. The tip of the probe was placed 4.5 mm away from the disk edge and it was moved outwards along 1 mm in 25-µm steps using a linear stage. In each step, the voltage of the photodetector was recorded. This procedure was repeated three times for each distance, and the standard deviation of the three measurements was calculated. The final uncertainty of each sensor (see Table 1) was obtained as the average of all the standard deviations for each distance.

Results
As mentioned in the previous section, the objective of the tests is to experimentally characterize the vibrational behavior of a rotating disk (first prototype) in a realistic operation condition. In this way, the manufacturer could optimize some parameters of the disk to reduce the vibrations in an upgraded design (second prototype). Figure 6 shows the signals and their FFTs obtained for the case of the first prototype of the disk. The signals were obtained from OFS 1, which was placed on the upper part of the wind tunnel, in the direction of an imaginary vertical axis that passes by the center of the disk. OFS 2 and OFS 3 were placed forming angles of 120 • and −120 • with the direction of OFS 1, respectively. The graphs correspond to a pressure difference of 2.5 bar when the disk is rotating at nominal speed (c and d), and when it is not rotating (a and b). Notice that the airflow forces the disk to flutter even when it is static. Even in such a case, the TC varies substantially with the vibration of the disk, and the vibration frequency is easily identified by the peak in the FFT of the signal. The signal in the time domain becomes more complex when the disk is rotating, and its FFT shows that more vibration frequencies than in the static condition are detected. standard deviation of the three measurements was calculated. The final uncertainty of each sensor (see Table 1) was obtained as the average of all the standard deviations for each distance. Sensor Uncertainty (µm) 1 7 2 7 3 10

Results
As mentioned in the previous section, the objective of the tests is to experimentally characterize the vibrational behavior of a rotating disk (first prototype) in a realistic operation condition. In this way, the manufacturer could optimize some parameters of the disk to reduce the vibrations in an upgraded design (second prototype). Figure 6 shows the signals and their FFTs obtained for the case of the first prototype of the disk. The signals were obtained from OFS 1, which was placed on the upper part of the wind tunnel, in the direction of an imaginary vertical axis that passes by the center of the disk. OFS 2 and OFS 3 were placed forming angles of 120° and −120° with the direction of OFS 1, respectively. The graphs correspond to a pressure difference of 2.5 bar when the disk is rotating at nominal speed (c and d), and when it is not rotating (a and b). Notice that the airflow forces the disk to flutter even when it is static. Even in such a case, the TC varies substantially with the vibration of the disk, and the vibration frequency is easily identified by the peak in the FFT of the signal. The signal in the time domain becomes more complex when the disk is rotating, and its FFT shows that more vibration frequencies than in the static condition are detected.  The results obtained for the first prototype at various rotational speeds are summarized in Tables 2-5. To calculate the amplitude of the vibrations, the TC of the disk is expressed in terms of its change, hence the negative values shown in Figure 6c. While the frequency of the strain gauge installed on the disk surface represents the real vibration frequency of the disk in every case, the frequency of the OFSs (f os ) is modulated by the rotational speed of the disk and by the NDs. Thus, the vibration frequency of the disk provided by the OFS (f disk ) has to be obtained by demodulating f os using Equation (1). The only exception is the case in which the disk is not rotating, since the frequencies of the signals from the strain gauge and from the OFSs coincide. All vibration frequencies provided by the OFSs match one another, and they also match those given by the strain gauge. The corresponding amplitudes are not correlated, since they correspond to vibrations measured at different points of the disk. For a fixed rotational speed, the amplitude of each vibration increases as the pressure difference between both sides of the disk becomes higher (see Figure 7). A situation that is worthy of study can be seen in Figure 7, in the case when the pressure difference is 2.6 bar and the disk is turning at RPM nominal . In such a case, the vibration frequency of the disk is markedly different, because it passes from 2247 Hz to 1574 Hz (2122 Hz to 1474 Hz for the frequency detected by the OFS). This is due to a change in the way this disk vibrates: for the lower pressure differences, the disk vibrates with five nodal diameters whereas at 2.6 bar the disk vibrates with ND = 4. The value of ND can be obtained from Equation (1), since f disk only matches the correct vibration frequency, which is given by the strain gauge, when the correct value of ND is used to demodulate f os . A similar behavior can be observed when the disk is rotating at 1.5 × RPM nominal , and at 2 × RPM nominal , with the peculiarity that it happens at lower pressure difference: 2.4 bar for 1.5 × RPM nominal and 2.2 bar for 2 × RPM nominal . The results obtained for the first prototype at various rotational speeds are summarized in Tables 2-5. To calculate the amplitude of the vibrations, the TC of the disk is expressed in terms of its change, hence the negative values shown in Figure 6c. While the frequency of the strain gauge installed on the disk surface represents the real vibration frequency of the disk in every case, the frequency of the OFSs (fos) is modulated by the rotational speed of the disk and by the NDs. Thus, the vibration frequency of the disk provided by the OFS (fdisk) has to be obtained by demodulating fos using Equation (1). The only exception is the case in which the disk is not rotating, since the frequencies of the signals from the strain gauge and from the OFSs coincide. All vibration frequencies provided by the OFSs match one another, and they also match those given by the strain gauge. The corresponding amplitudes are not correlated, since they correspond to vibrations measured at different points of the disk. For a fixed rotational speed, the amplitude of each vibration increases as the pressure difference between both sides of the disk becomes higher (see Figure 7). A situation that is worthy of study can be seen in Figure 7, in the case when the pressure difference is 2.6 bar and the disk is turning at RPMnominal. In such a case, the vibration frequency of the disk is markedly different, because it passes from 2247 Hz to 1574 Hz (2122 Hz to 1474 Hz for the frequency detected by the OFS). This is due to a change in the way this disk vibrates: for the lower pressure differences, the disk vibrates with five nodal diameters whereas at 2.6 bar the disk vibrates with ND = 4. The value of ND can be obtained from Equation (1), since fdisk only matches the correct vibration frequency, which is given by the strain gauge, when the correct value of ND is used to demodulate fos. A similar behavior can be observed when the disk is rotating at 1.5 × RPMnominal, and at 2 × RPMnominal, with the peculiarity that it happens at lower pressure difference: 2.4 bar for 1.5 × RPMnominal and 2.2 bar for 2 × RPMnominal.   To better appreciate the improvement in the second prototype, the amplitude and frequency of the most similar working points for both prototypes have been depicted in Figure 8a were acquired with the disk in an initial position of 0° and with the disk rotated 90° and 202.5° with respect to this initial position. Figure 9a depicts the results for the three positions of the disk. As expected, the differences between the circumferences are very small. Their corresponding centers differ from the theoretical one in less than 0.65 mm, as can be seen in Figure 9b. This distance means a shift of the center of about 0.2% of the circumference radius, which makes it quite difficult to distinguish each circumference in Figure 9a.  Another important improvement detected in the second prototype is the absence of changes in the way the disk was vibrating. There was no change in the number of nodal diameters of the disk. The second prototype vibrates with ND = 5 when the disk is not rotating and with ND = 3 for the rest of rotational speeds, independently of the rotational speed. Therefore, a more uniform and less complex vibrational behavior was achieved for this prototype.
The fact that three OFSs were employed allows us to determine the eccentricity of the disk. The circumference corresponding to the disk was calculated from the three TC measurements provided by each OFS when the disk is static. The lowest pressure difference (2.3 bar) was used to measure the eccentricity, so that the influence of the vibration in the measurement was minimum. The TC value was obtained as the mean value of the signal for an acquisition time of five seconds. The three TC points define a unique circumference, whose equation is easily calculated by solving the following system of equations to find A, B and C. Where x OFSi and y OFSi are the values obtained by subtracting the TC variation measurement of each sensor from the initial distance of the disk.
x 2 OFS1 + y 2 OFS1 + Ax OFS1 + By OFS1 + C = 0 (5) x 2 OFS2 + y 2 OFS2 + Ax OFS2 + By OFS2 + C = 0 (6) x 2 OFS3 + y 2 OFS3 + Ax OFS3 + By OFS3 + C = 0 The eccentricity of the disk was determined in three different positions: the TC measurements were acquired with the disk in an initial position of 0 • and with the disk rotated 90 • and 202.5 • with respect to this initial position. Figure 9a depicts the results for the three positions of the disk. As expected, the differences between the circumferences are very small. Their corresponding centers differ from the theoretical one in less than 0.65 mm, as can be seen in Figure 9b. This distance means a shift of the center of about 0.2% of the circumference radius, which makes it quite difficult to distinguish each circumference in Figure 9a. (a) (b) Figure 8. Vibration amplitude (a) and frequency (b) for the first Prototype (black) and the second Prototype (red) obtained by OFS 1 for the most similar working points (squares correspond to 0 rpm, circles to RPMnominal, triangles to 1.5 × RPMnominal and diamonds to 2 × RPMnominal).

Conclusions
The vibrational behavior of a rotating disk has been studied from the tip-clearance measurements provided by three optical fiber sensors. This disk is a model of a real aircraft engine component. It was installed in a wind tunnel, where real working conditions were simulated. Although the sensors were initially designed to perform the TC measurements in low pressure turbines, the configuration was adapted to successfully perform these measurements in the rotating disk. A first prototype of the disk was completely characterized by identifying not only the amplitude and frequency of the vibration, but also the number of nodal diameters of the disk and its variations during the tests. All this valuable information allowed the disk manufacturer to design an upgraded prototype of the disk. This, in turn, was also characterized by examining its vibrational behavior in order to assess the improvements in performance. The obtained results have confirmed a clear improvement in the design of the component. Therefore, the suitability of this innovative optical system both to characterize and to improve rotating disks has also been demonstrated.